// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "matrix_functions.h"

double
binom(int n, int k)
{
	double res = 1;
	for (int i = 0; i < k; i++)
		res = res * (n - k + i + 1) / (i + 1);
	return res;
}

template<typename T>
T
expfn(T x, int)
{
	return std::exp(x);
}

template<typename T>
void
test2dRotation(double tol)
{
	Matrix<T, 2, 2> A, B, C;
	T angle;

	A << 0, 1, -1, 0;
	for (int i = 0; i <= 20; i++) {
		angle = static_cast<T>(pow(10, i / 5. - 2));
		B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle);

		C = (angle * A).matrixFunction(expfn);
		std::cout << "test2dRotation: i = " << i << "   error funm = " << relerr(C, B);
		VERIFY(C.isApprox(B, static_cast<T>(tol)));

		C = (angle * A).exp();
		std::cout << "   error expm = " << relerr(C, B) << "\n";
		VERIFY(C.isApprox(B, static_cast<T>(tol)));
	}
}

template<typename T>
void
test2dHyperbolicRotation(double tol)
{
	Matrix<std::complex<T>, 2, 2> A, B, C;
	std::complex<T> imagUnit(0, 1);
	T angle, ch, sh;

	for (int i = 0; i <= 20; i++) {
		angle = static_cast<T>((i - 10) / 2.0);
		ch = std::cosh(angle);
		sh = std::sinh(angle);
		A << 0, angle * imagUnit, -angle * imagUnit, 0;
		B << ch, sh * imagUnit, -sh * imagUnit, ch;

		C = A.matrixFunction(expfn);
		std::cout << "test2dHyperbolicRotation: i = " << i << "   error funm = " << relerr(C, B);
		VERIFY(C.isApprox(B, static_cast<T>(tol)));

		C = A.exp();
		std::cout << "   error expm = " << relerr(C, B) << "\n";
		VERIFY(C.isApprox(B, static_cast<T>(tol)));
	}
}

template<typename T>
void
testPascal(double tol)
{
	for (int size = 1; size < 20; size++) {
		Matrix<T, Dynamic, Dynamic> A(size, size), B(size, size), C(size, size);
		A.setZero();
		for (int i = 0; i < size - 1; i++)
			A(i + 1, i) = static_cast<T>(i + 1);
		B.setZero();
		for (int i = 0; i < size; i++)
			for (int j = 0; j <= i; j++)
				B(i, j) = static_cast<T>(binom(i, j));

		C = A.matrixFunction(expfn);
		std::cout << "testPascal: size = " << size << "   error funm = " << relerr(C, B);
		VERIFY(C.isApprox(B, static_cast<T>(tol)));

		C = A.exp();
		std::cout << "   error expm = " << relerr(C, B) << "\n";
		VERIFY(C.isApprox(B, static_cast<T>(tol)));
	}
}

template<typename MatrixType>
void
randomTest(const MatrixType& m, double tol)
{
	/* this test covers the following files:
	   Inverse.h
	*/
	typename MatrixType::Index rows = m.rows();
	typename MatrixType::Index cols = m.cols();
	MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);

	typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;

	for (int i = 0; i < g_repeat; i++) {
		m1 = MatrixType::Random(rows, cols);

		m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
		std::cout << "randomTest: error funm = " << relerr(identity, m2);
		VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));

		m2 = m1.exp() * (-m1).exp();
		std::cout << "   error expm = " << relerr(identity, m2) << "\n";
		VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
	}
}

EIGEN_DECLARE_TEST(matrix_exponential)
{
	CALL_SUBTEST_2(test2dRotation<double>(1e-13));
	CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
	CALL_SUBTEST_8(test2dRotation<long double>(1e-13));
	CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
	CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
	CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14));
	CALL_SUBTEST_6(testPascal<float>(1e-6));
	CALL_SUBTEST_5(testPascal<double>(1e-15));
	CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
	CALL_SUBTEST_7(randomTest(Matrix<double, 3, 3, RowMajor>(), 1e-13));
	CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
	CALL_SUBTEST_4(randomTest(MatrixXd(8, 8), 1e-13));
	CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
	CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
	CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
	CALL_SUBTEST_6(randomTest(MatrixXf(8, 8), 1e-4));
	CALL_SUBTEST_9(randomTest(Matrix<long double, Dynamic, Dynamic>(7, 7), 1e-13));
}
